A) Field of the Invention
The present invention relates to a projection method using a charged particle beam, and more particularly to a projection method involving proximity effect correction for improving a precision of a pattern size after developing.
B) Description of the Related Art
Patterns to be formed are becoming finer because of recent improvements on an integration degree of semiconductor integrated circuit devices, and a resolution of a conventional optical projection is insufficient nowadays. In order to form a fine pattern, a projection using a charged particle beam, particularly an electron beam, is used.
An electron beam projection method is classified into a point beam projection, a variable shaped beam projection, a character projection and an electron projection lithography. With the point beam projection, an area to be exposed is scanned with an electron beam having a dot-shaped beam spot, and a high resolution can be obtained. On the other hand, it is difficult to obtain a high throughput. With the variable shaped beam projection, a pattern to be exposed is divided into small rectangular unit areas to perform exposure with respect to each unit area. As compared to the point beam projection, the variable shaped beam projection can effect a higher throughput.
With the character projection, a stencil mask having some repetitive patterns thereon is used and one-shot exposure is performed with respect to each pattern on the stencil. Similar to an optical projection, the electron projection lithography uses a mask corresponding to a pattern to be transferred to perform a one-shot exposure for a large area. As compared to the variable shaped beam projection, the character projection and electron projection lithography can reduce the number of electron beam shots, and can improve further a throughput.
While an electron beam is irradiated to a resist film on a substrate to print a circuit pattern, a portion of the electron beam incident upon the resist film is forward-scattered and a portion of the electron beam transmitted through the resist film is backscattered and becomes again incident upon the resist film. Therefore, even if an electron beam is made incident upon one point on the resist film, the effect of the electron beam incidence spreads and so-called proximity effect occurs.
An exposure intensity distribution function (hereinafter called an “EID function”) for a resist film when an electron beam is made incident upon one point (x, y) on the resist film is expressed by the following equation in which a forward-scattering term and a backscattering term are approximated by Gaussian distributions:
                              f          ⁡                      (                          x              ,              y                        )                          =                              1                          π              ⁡                              (                                  1                  +                  η                                )                                              ⁢                      {                                                            1                                      β                    f                    2                                                  ⁢                                  exp                  ⁡                                      (                                          -                                                                                                    x                            2                                                    +                                                      y                            2                                                                                                    β                          f                          2                                                                                      )                                                              +                                                η                                      β                    b                    2                                                  ⁢                                  exp                  ⁡                                      (                                          -                                                                                                    x                            2                                                    +                                                      y                            2                                                                                                    β                          b                          2                                                                                      )                                                                        }                                              (        1        )            where βf represents a forward-scattering length, βb represents a backscattering length and η represents a ratio of a backscattering energy to a forward-scattering energy (hereinafter called a backscattering ratio). The first term of the right side of the equation (1) is called a forward-scattering term and the second term is called a backscattering term. The forward-scattering has a large influence on a narrow area, whereas the backscattering has a small influence on a broad area. A ratio between these influences is the backscattering ratio η. These values are dependent upon an electron beam energy, a resist film thickness, a substrate material and the like, and are determined from exposure evaluation experiments or computer simulation. As an acceleration energy of an electron beam becomes high, the forward-scattering length βf becomes short and the backscattering length βb becomes long.
A conventional proximity effect correction method sets evaluation points at a center point and corners of each side of each pattern to be exposed, and calculates a deposition energy at each evaluation point when the pattern is exposed, by using the equation (1). A difference between a calculated value and a target value is calculated at each of a plurality of evaluation points, and an exposure dose is determined so as to minimize a square sum of the differences.
As the number of patterns increases greatly because of high integration of semiconductor integrated circuit devices, the above-described calculations take a long time. The proximity effect correction method has been desired which can shorten the calculation time and can set a size error of a developed pattern (finished pattern) in an allowable range.
As one example of the correction methods to meet the above requirements, “Fast proximity effect correction method using a pattern area density map” by F. Murai, et al., J. Vac. Sci. Technol. B, Vol. 10, No. 6 (1992), pp. 3072 to 3076 (Document 1) discloses a proximity effect correction method (hereinafter called a “pattern area density method”) using a pattern area density map obtained by dividing a pattern layout plane into a plurality of rectangular small regions by a square lattice.
A spread of the forward-scattering is sufficiently smaller than a pattern pitch. Therefore, in order to obtain a deposition energy based on the forward-scattering term at an arbitrary point, it is only necessary to integrate the forward-scattering term of the equation (1) in an area of one pattern to be exposed. In this specification, an energy accumulated in a resist film is called a “deposition energy”. The deposition energy is generally represented by the unit of “eV/cm3”.
The backscattering influences a broader area than the forward-scattering. Therefore, the integration area of the backscattering term of the equation (1) is required to cover not only the target pattern but also a large number of nearby patterns. The calculation amount becomes therefore massive. In order to prevent an increase in the calculation amount, the deposition energy based on backscattered electrons is calculated by the pattern area density method. The pattern area density method will be described hereunder.
First, an exposure pattern layout plane is divided into a plurality of rectangular small regions by a square lattice having a fixed size. An area density of each small region is calculated. The term “area density” means a ratio of an area occupied by a pattern in the small region to the whole area of the small region. The size of the small region is set in such a manner that the deposition energy based on the backscattered electrons can be approximated generally constant in each of the small regions. The pattern area density map can therefore be obtained, having a correspondence between each small region and its area density.
Next, a deposition energy at the center point in a target small region is calculated, the deposition energy being generated by backscattering of electron beams incident upon the target small region and nearby small regions. This process is called “smoothing of the pattern area density map”.
In the smoothing, it is assumed that a virtual electron beam having a uniform intensity is incident upon the whole area of each small region. An integrated value of the exposure dose of each small region by the virtual electron beam is equal to an integrated value of the exposure dose for the case where a pattern in the small region is exposed. Since it is assumed that the small region is uniformly exposed, the calculation amount can be reduced more than that of a numerical integration of the backscattering term of the equation (1).
It is therefore possible to calculate the deposition energy at the center point of each small region by the influence of backscattering. The deposition energy based on the backscattering at the center point of a small region is added to the deposition energy based on the forward-scattering in the pattern of the small region. A proper exposure dose of each small region can be calculated by considering the influences of forward-scattering and backscattering.
JP-A-2001-52999 discloses a method for correcting exposure dose using the pattern area density method to improve a pattern size precision after development. This method is applied to the variable shaped beam projection and character projection. JP-A-2002-313693 discloses a method for correcting the mask pattern size using the pattern area density method to improve a pattern size precision after development. This method is applied mainly to the electron projection lithography.
JP-A-2005-101501 discloses a method for calculating a deposition energy based on backscattering at high precision, by considering electron scattering in a plurality of layers under a resist film.
The EID function of the equation (1) does not reflect sufficiently the scattering effect in an actual structure constituted of a resist film to be exposed and a substrate. Therefore, as a pattern is made finer, the pattern size after development may shift from a target pattern size even if the exposure by the method disclosed in JP-A-2001-52999 or the method disclosed in JP-A-2002-313693 is performed.
An example of the EID function precisely reflecting the influence of electron scattering and the like occurring in an actual structure to be exposed is disclosed in “Point exposure distribution measurements for proximity correction in electron beam lithography on a sub-100 nm scale”, S. A. Rishton et al., J. Vac. Sci. Technol. B, Vol. 5, No. 1 (1987), pp. 135 to 141 (document 2) and “Estimation of Optimum Electron Projection Lithography Mask Biases Taking Coulomb Beam Blur into Consideration”, Jpn. J. Appl. Phys. Vol. 42 (2003), pp. 3816 to 3821 (Document 3). Document 2 discloses a method of approximating the EID function by a plurality of Gaussian distributions, and Document 3 discloses a method of approximating the EID function by Gaussian distributions and exponential distributions. These EID functions take into consideration not only the influence of patterns adjacent to the target pattern but also the influence of patterns remote from the target pattern.